Lipschitz Conditions in Damek–Ricci Spaces

Abstract

In this paper we extend classical Titchmarsh theorems on the Fourier–Helgason transform of Lipschitz functions to the setting of $L^{p}$-space on Damek–Ricci spaces. As consequences, quantitative Riemann–Lebesgue estimates are obtained and an integrability result for the Fourier–Helgason transform is developed extending ideas used by Titchmarsh in the one dimensional setting.